We find the x-intercept of the curve

For \(y=o\) we have \(\displaystyle={0}\frac{{x}}{{{\left({x}-{1}\right)}{\left({x}+{3}\right)}}}\Rightarrow{x}={0}\)

\(\displaystyle\therefore\) The curve touches at the point (0,0)

ext we find y-intercept of the curve

For \(x=0\) we have \(y=0\)

\(\displaystyle\therefore\) The curve touches the point (0)

Now, the vertical asymptotes of the curve are

\(\displaystyle{x}-{1}={0}\Rightarrow{x}={1}\)

\(\displaystyle{x}+{3}={0}\Rightarrow{x}=-{3}\)